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Evolution of a Random Vortex Filament, The

Bessaih, Hakima
; 
Gubinelli, M.
; 
Russo, F.
Abstract
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We study an evolution problem in the space of continuous loops in a three-dimensional Euclidean space modeled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting from Holder regular loops with index greater than 1/3. When the Holder regularity of the initial condition X is smaller or equal to 1/2, we require X to be a rough path in the sense of Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310, System Control and Rough Paths (2002). Oxford Univ. Press]. The solution will then live in an appropriate space of rough paths. In particular, we can construct (local) solution starting from almost every Brownian loop.
Date
2005-09-01
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University of Wyoming. Libraries
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Keywords
vortex filaments,rough path theory,path-wise stochastic integration,Mathematics
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https://wyoscholar.uwyo.edu/handle/internal/1699
 https://doi.org/10.15786/wyoscholar/9774
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Faculty Publications | Mathematics and Statistics
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